Problem: What's the first wrong statement in the proof below that $ \triangle CAB \cong \triangle CEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \angle DBE \cong \angle ABC$ $, \ $ $ \angle CFE \cong \angle ABC$ $, \ $ $ \overline{EF} \cong \overline{AB}$ $, \ $ and $\ $ $ \angle CEF \cong \angle BAC$ Proof $ \triangle CAB \cong \triangle DEB$ because AAS $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \angle CBE \cong \angle ECF$ because corresponding parts of congruent triangles are congruent $ \triangle CAB \cong \triangle CEF$ because ASA $ \overline{AC} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle CAB \cong \triangle CEB$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle ECF \cong \angle CBE$ is the first wrong statement.